$2.$ The startup AndersonVenture had an A$-$round in which it sold $10$ million shares of convertible preferred stock at $$1\mathrm{.}00$ per share. Prior to the Series A financing, Management owned $15$ million shares of common stock and the Conversion Price of preferred stock to common stock was $1$:$1.$ AndersonVenture needs to raise an additional $$5$ million in a series B round and learns that new investors insist on a pre$-$money valuation of $$15$ million. Please create a fully diluted capitalization table after the Series B investment, under three scenarios:

a$.$ There is no dilution protection for prior investors.

b$.$ There is full ratchet protection.

c$.$ There is weighted average dilution protection.